This thesis presents a methodology to estimate the parameters of single-phase induction motors (SPIMs). The parameter estimates are suitable to model the responses of SPIMs in both steadystate and transient conditions. Firstly, they are calculated from multiple sets of steady-state test-based measurements using the Newton-Raphson (NR) method. The NR-based algorithm iteratively solves a system of non-linear equations involving the parameter values of leakage inductances, magnetizing inductance, and rotor resistance. Selected parameters are further tuned based on a non-linear least squares (NLS) formulation that minimizes the mismatch between modeled and measured outputs during the start-up transients. The NLS problem is solved using the workhorse algorithm for this application, namely the Levenberg-Marquardt (L-M) update. Per iteration, the L-M update direction for the parameter values follows from both the gradient direction and the Gauss-Newton one. Having parameter values obtained by the first two algorithms, the third algorithm tracks the start capacitance of SPIMs, a time-varying parameter. This is achieved using recursive extended Kalman filtering (EKF) after augmenting the motor state vector with a constant capacitance state. EKF recursively linearizes the augmented system and estimates the full augmented state vector. The last two proposed algorithms only need to collect motor terminal data during normal transient operations such as start-up. This non-intrusive feature makes them ideal for online applications such as capacitor prognostics. The effectiveness of the estimation methodology has been demonstrated and validated using both simulation and real data. Lastly, a research outlook aiming at simplifying the capacitor prognostic method is also presented, by investigating the relationship between capacitance and current magnitude.